QCD at Finite Density and Color Superconductivity

Brief review of current status of the field.Comment: Invited talk at Lattice 99, Pisa, July 1999. 5 pages, 7 fig

Mass Terms in Effective Theories of High Density Quark Matter

We study the structure of mass terms in the effective theory for quasi-particles in QCD at high baryon density. To next-to-leading order in the $1/p_F$ expansion we find two types of mass terms, chirality conserving two-fermion operators and chirality violating four-fermion operators. In the effective chiral theory for Goldstone modes in the color-flavor-locked (CFL) phase the former terms correspond to effective chemical potentials, while the latter lead to Lorentz invariant mass terms. We compute the masses of Goldstone bosons in the CFL phase, confirming earlier results by Son and Stephanov as well as Bedaque and Sch\"afer. We show that to leading order in the coupling constant $g$ there is no anti-particle gap contribution to the mass of Goldstone modes, and that our results are independent of the choice of gauge.Comment: 22 pages, 4 figure

Superdense Matter

We review recent work on the phase structure of QCD at very high baryon density. We introduce the phenomenon of color superconductivity and discuss the use of weak coupling methods. We study the phase structure as a function of the number of flavors and their masses. We also introduce effective theories that describe low energy excitations at high baryon density. Finally, we study the possibility of kaon condensation at very large baryon density.Comment: 13 pages, talk at ICPAQGP, Jaipur, India, Nov. 26-30, 2001; to appear in the proceeding

Instanton Effects in QCD at High Baryon Density

We study instanton effects in QCD at very high baryon density. In this regime instantons are suppressed by a large power of $(\Lambda_{QCD}/\mu)$, where $\Lambda_{QCD}$ is the QCD scale parameter and $\mu$ is the baryon chemical potential. Instantons are nevertheless important because they contribute to several physical observables that vanish to all orders in perturbative QCD. We study, in particular, the chiral condensate and its contribution $m_{GB}^2\sim m$ to the masses of Goldstone bosons in the CFL phase of QCD with $N_f=3$ flavors. We find that at densities $\rho\sim (5-10) \rho_0$, where $\rho_0$ is the density of nuclear matter, the result is dominated by large instantons and subject to considerable uncertainties. We suggest that these uncertainties can be addressed using lattice calculations of the instanton density and the pseudoscalar diquark mass in QCD with two colors. We study the topological susceptibility and Witten-Veneziano type mass relations in both $N_c=2$ and $N_c=3$ QCD.Comment: 27 pages, 8 figures, minor revision

Instantons and Scalar Multiquark States: From Small to Large N_c

We study scalar quark-anti-quark and two-quark-two-anti-quark correlation functions in the instanton liquid model. We show that the instanton liquid supports a light scalar-isoscalar (sigma) meson, and that this state is strongly coupled to both $(\bar{q}q)$ and $(\bar{q}q)^2$. The scalar-isovector $a_0$ meson, on the other hand, is heavy. We also show that these properties are specific to QCD with three colors. In the large $N_c$ limit the scalar-isoscalar meson is not light, and it is mainly coupled to $(\bar{q}q)$.Comment: 24 page

Phases of QCD at High Baryon Density

We review recent work on the phase structure of QCD at very high baryon density. We introduce the phenomenon of color superconductivity and discuss how the quark masses and chemical potentials determine the structure of the superfluid quark phase. We comment on the possibility of kaon condensation at very high baryon density and study the competition between superfluid, density wave, and chiral crystal phases at intermediate density.Comment: 15 pages. To appear in the proceedings of the ECT Workshop on Neutron Star Interiors, Trento, Italy, June 200

The Shear Viscosity to Entropy Density Ratio of Trapped Fermions in the Unitarity Limit

We extract the shear viscosity to entropy density ratio \eta/s of cold fermionic atoms in the unitarity limit from experimental data on the damping of collective excitations. We find that near the critical temperature \eta/s is roughly equal to 1/2 in units of \hbar/k_B. With the possible exception of the quark gluon plasma, this value is closer to the conjectured lower bound 1/(4\pi) than any other known liquid.Comment: published versio

The Kohn-Luttinger Effect in Gauge Theories

Kohn and Luttinger showed that a many body system of fermions interacting via short range forces becomes superfluid even if the interaction is repulsive in all partial waves. In gauge theories such as QCD the interaction between fermions is long range and the assumptions of Kohn and Luttinger are not satisfied. We show that in a U(1) gauge theory the Kohn-Luttinger phenomenon does not take place. In QCD attractive channels always exist, but there are cases in which the primary pairing channel leaves some fermions ungapped. As an example we consider the unpaired fermion in the 2SC phase of QCD with two flavors. We show that it acquires a very small gap via a mechanism analogous to the Kohn-Luttinger effect. The gap is too small to be phenomenologically relevant.Comment: 5 pages, 2 figure, minor revisions, to appear in PR